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8-1
PowerPoint Presentation by PowerPoint Presentation by Douglas CloudDouglas Cloud
Professor Emeritus of AccountingProfessor Emeritus of AccountingPepperdine UniversityPepperdine University
© Copyright 2007 Thomson South-Western, a part of The Thomson Corporation. Thomson,
the Star Logo, and South-Western are trademarks used herein under license.
Task Force Image Gallery clip art included in this electronic presentation is used with the
permission of NVTech Inc.
Task Force Image Gallery clip art included in this electronic presentation is used with the
permission of NVTech Inc.
Financial AccountingInformation for Decisions
6th edition
Ingram and Albright
F1388The Time The Time Value of Value of MoneyMoney
Financial AccountingA Bridge to Decision MakingA Bridge to Decision Making
Ingram and Albright
6th edition
8-2
ObjectivesObjectivesObjectivesObjectives
Once you have completed this chapter, you should be able to—
Once you have completed this chapter, you should be able to—
8-3
1. Define future and present value.
ObjectivesObjectivesObjectivesObjectives
2. Determine the future value of a single amount invested at the present time.
3. Determine the future value of an annuity.4. Determine the present value of a single amount
to be received in the future.5. Determine the present value of an annuity.6. Determine investment values and interest
expense or revenue for various periods.
8-4
11ObjectiveObjectiveObjectiveObjective
Determine future and present value.
8-5
Future ValueFuture ValueFuture ValueFuture Value
The future value of an amount is the value of that
amount at a particular time in
the future.
The future value of an amount is the value of that
amount at a particular time in
the future.
8-6
Future ValueFuture ValueFuture ValueFuture Value
The present value of an amount is the
value of that amount at a particular date
prior to the time the amount is paid or
received.
The present value of an amount is the
value of that amount at a particular date
prior to the time the amount is paid or
received.
8-7
Future ValueFuture ValueFuture ValueFuture Value
Future Value = Present Value (1 + R)
Interest Rate
8-8
Future ValueFuture ValueFuture ValueFuture Value
Future Value = Present Value (1 + R)
Future Value = $1,000(1.05)
If $1,000 is invested on January 1, 2007, at 5% interest, what will be the future value
(the amount that will accumulate) by December 31, 2007?
If $1,000 is invested on January 1, 2007, at 5% interest, what will be the future value
(the amount that will accumulate) by December 31, 2007?
Future Value = $1,050
8-9
22Determine the future value of a single amount invested at the present time.
ObjectiveObjectiveObjectiveObjective
8-10
Compound InterestCompound InterestCompound InterestCompound Interest
If the accumulated amount ($1,050) is left in the savings account for a second year, until December 31,
2008, how much would the investment be worth at that time?
If the accumulated amount ($1,050) is left in the savings account for a second year, until December 31,
2008, how much would the investment be worth at that time?
FV = $1,050(1.05)FV = $1,102.50
8-11
Compound InterestCompound InterestCompound InterestCompound Interest
Interest earned in one period on interest earned in an earlier period is known as compound interest.
Interest earned in one period on interest earned in an earlier period is known as compound interest.
8-12
Compound InterestCompound InterestCompound InterestCompound Interest
Assume you invest $500 for three years at 8% interest. How much would your investment
be worth at the end of three years?
Assume you invest $500 for three years at 8% interest. How much would your investment
be worth at the end of three years?
FV = PV(1 + R)t
FV = $500(1.08)³
FV = $500(1.08)(1.08)(1.08)
FV = $629.86
8-13
To calculate a future value, a future value of a single amount
table, such as the one in the next slide, can be used.
To calculate a future value, a future value of a single amount
table, such as the one in the next slide, can be used.
Compound InterestCompound InterestCompound InterestCompound Interest
8-14
Compound InterestCompound InterestCompound InterestCompound Interest
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09PeriodInterest RateInterest Rate
1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090
1.020 1.040 1.061 1.082 1.103 1.224 1.145 1.664 1.188
1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295
1
2
3
Future Value of a Single Amount
Note: Due to space limitations, the tables in this chapter have the table values rounded to three decimal places.
8-15
Compound InterestCompound InterestCompound InterestCompound Interest
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period
1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090
1.020 1.040 1.061 1.082 1.103 1.224 1.145 1.664 1.188
1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295
1
2
3
Interest RateInterest Rate
1.2601.260
FV = $500 x 1.260 = $630 (rounded)
8-16
Interest Table for an Investment of $500 for Three Years at 8%
A B C DA B C D
Value atValue at Interest EarnedInterest Earned FV at YearendFV at YearendYearYear Beginning of YearBeginning of Year (B x Interest Rate)(B x Interest Rate) (B + C)(B + C)
1 500.00 40.00 540.00
2 540.00 43.20 583.20
3 583.20 46.66 629.86
TotalTotal 129.86129.86
Exhibit 1Exhibit 1Exhibit 1Exhibit 1
8-17
Exercise 8-2Exercise 8-2Exercise 8-2Exercise 8-2
Click the button to skip this exercise.If you experience trouble making the button work, type 20 and press “Enter.”
Assume that you borrow $25,000 on April 1, 2007, at an annual rate of 7%. How much will you owe on March 31, 2008 if you make no payments until that date?
Press “Enter” or left click the mouse for solution.
FV = $25,000 x (1.07) = $26,7501
ContinuedContinuedContinuedContinued
8-18
Exercise 8-2Exercise 8-2Exercise 8-2Exercise 8-2
How much will you owe on March 31, 2009 if you make no payments until that date?
FV = $25,000 x (1.07) = $28,622.502
ContinuedContinuedContinuedContinued
Press “Enter” or left click the mouse for solution.
8-19
Exercise 8-2Exercise 8-2Exercise 8-2Exercise 8-2
If you pay the interest incurred for the first year on March 31, 2008, how much will you owe on March 31, 2009 if you make no other payments until that date?
FV = $25,000 x (1.07) = $26,7501
If the interest incurred during the first year is paid off before the second year begins, interest will
accrue only on the $25,000 during Year 2.
Press “Enter” or left click the mouse for solution.
8-20
33Determine the future value of an annuity.
ObjectiveObjectiveObjectiveObjective
8-21
An annuity is a series of equal amounts received or
paid over a specified number of equal time periods.
An annuity is a series of equal amounts received or
paid over a specified number of equal time periods.
Future Value of an AnnuityFuture Value of an AnnuityFuture Value of an AnnuityFuture Value of an Annuity
8-22
If $500 is invested at the end of each year for three years, how much
would the investment be worth at the end of three years if the interest
earned is 8% per year?
If $500 is invested at the end of each year for three years, how much
would the investment be worth at the end of three years if the interest
earned is 8% per year?
Future Value of an AnnuityFuture Value of an AnnuityFuture Value of an AnnuityFuture Value of an Annuity
8-23
Future Value of an AnnuityFuture Value of an AnnuityFuture Value of an AnnuityFuture Value of an Annuity
End of Year 1 End of Year 2 End of Year 3 FV at End of Year 3
Invested for 2 years ($500 x 1.08²) $ 583.20
Invested for 1 years ($500 x 1.08¹) 540.00
Invested for 0 years 500.00
Future value of total investment $1,623.20
Total amount invested over 2 years 1,500.00
Interest earned over 2 years
$ 123.20
8-24
Future Value of an AnnuityFuture Value of an AnnuityFuture Value of an AnnuityFuture Value of an Annuity
1
2
3
Interest RateInterest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090
3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.2783.2463.246
FVA = Amount invested (A) x Interest factor (IF)FVA = $500 x 3.246 (rounded to three decimal places) FVA = $1,623 (or $1,623.20 if a four-decimal table is
used)
8-25
A B C D EA B C D E
Value Value Interest EarnedInterest Earned AmountAmount FV at FV at at Beginningat Beginning (Column B x(Column B x Invested atInvested at End of End of
Year Year of Yearof Year Interest Rate)Interest Rate) End of YearEnd of Year YearYear
1 0.00 0.00 500.00 500.00
2 500.00 40.00 500.00 1,040.00
3 1,040.00 83.20 500.00 1,623.20
TotalTotal 123.20123.20 1,500.001,500.00
Interest Table for an Annuity of $500 at the End of Each Year for Three Years at 8%
Exhibit 2Exhibit 2Exhibit 2Exhibit 2
8-26
Future Value of an AnnuityFuture Value of an AnnuityFuture Value of an AnnuityFuture Value of an Annuity
How much would you need to invest each year to accumulate $1,000 at the
end of three years to take a trip to Mexico after you graduate from
college? Assume you can earn 6% on your investment.
How much would you need to invest each year to accumulate $1,000 at the
end of three years to take a trip to Mexico after you graduate from
college? Assume you can earn 6% on your investment.
8-27
Future Value of an AnnuityFuture Value of an AnnuityFuture Value of an AnnuityFuture Value of an Annuity
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090
3.030 3.060 3.091 3.122 3.153 1.191 1.225 1.260 1.295
1
2
3
Interest RateInterest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period
3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.2783
0.08
1.000
2.080
3.1843.184
FVA = Amount invested (A) x Interest factor (IF)$1,000 = A x 3.184 (using three decimal places) A = $1,000 ÷ 3.184 A = $314 (or $314.11 if 3.1836 is used)
8-28
Exercise 8-5Exercise 8-5Exercise 8-5Exercise 8-5
Click the button to skip this exercise.If you experience trouble making the button work, type 32 and press “Enter.”
Optimism, Inc. anticipates the need for factory expansion four years from today. The firm has determined that it will have the necessary funds for expansion if it puts $400,000 per year into a stock portfolio expected to earn 9% per year. Deposits will be made at the end of the year.
ContinuedContinuedContinuedContinued
8-29
Exercise 8-5Exercise 8-5Exercise 8-5Exercise 8-5
a) How much is the company planning to raise toward factory expansion with this plan?
Press “Enter” or left click the mouse for solution.
ContinuedContinuedContinuedContinued
FV of an annuity = Amount x Interest Factor= $400,000 x 4.57313= $1,829,252
9%, 4 years
8-30
Exercise 8-5Exercise 8-5Exercise 8-5Exercise 8-5
b) What amount would the company expect to raise if it could invest $400,000 per year for seven years?FV of an annuity = Amount x Interest Factor
= $400,000 x 9.20043= $3,680,172
9%, 7 years
Press “Enter” or left click the mouse for solution.
ContinuedContinuedContinuedContinued
8-31
Exercise 8-5Exercise 8-5Exercise 8-5Exercise 8-5
c) Why is the answer to part b more than twice as large as the answer to part a even though the length of the annuity is less than twice as long?
The future value of an annuity grows from the contribution of additional deposits and by the compounding of interest on the existing balances. In short, interest on interest contributes substantially to the annuity’s future value.
Press “Enter” or left click the mouse for solution.
8-32
44Determine the present value of a single amount to be received in the future.
ObjectiveObjectiveObjectiveObjective
8-33
Present Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single Amount
A company offered to sell you an investment that pays $3,000 at the end of three years. You want to
earn 8% return on your investment. How much would you be willing to
pay for the investment?
A company offered to sell you an investment that pays $3,000 at the end of three years. You want to
earn 8% return on your investment. How much would you be willing to
pay for the investment?
8-34
Present Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single Amount
FV = PV(1+R) t
$3,000 = PV(1+R)³
PV = $3,000 x 1/(1.08)³
PV = $3,000 ÷ (1.08)³ PV = $2,381.50
$3,000 = PV(1.08)³
8-35
Using Excel, the present value of an investment that pays $3,000 at the end of
three years at 8% can be calculated by entering =3000*(1/(1.08^3)) in a cell.
Using Excel, the present value of an investment that pays $3,000 at the end of
three years at 8% can be calculated by entering =3000*(1/(1.08^3)) in a cell.
Present Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single Amount
8-36
The present value of a single amount table also could be
used to determine the present value of the $3,000.
The present value of a single amount table also could be
used to determine the present value of the $3,000.
Present Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single Amount
8-37
0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917
0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842
1
2
3
Interest RateInterest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period
0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.7723
0.08
0.926
0.857
PV = FV x IFPV = $3,000 x 0.794 (rounded to three decimal places) PV = $2,381.49
Present Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single AmountPresent Value of a Single Amount
0.7940.794
8-38
Interest Table for a Present Value of $2,381.49 for Three Years at 8%
A B C DA B C D
Present Value atPresent Value at Interest EarnedInterest Earned Value at EndValue at EndYearYear Beginning of YearBeginning of Year (B x Interest Rate)(B x Interest Rate) (B + C)(B + C)
1 2,381.49 190.52 2,572.01
2 2,572.01 205.76 2,777.77
3 2,777.77 222.23 3,000.00
TotalTotal 618.51618.51
Exhibit 3Exhibit 3Exhibit 3Exhibit 3
8-39
Exercise 8-10Exercise 8-10Exercise 8-10Exercise 8-10
Click the button to skip this exercise.If you experience trouble making the button work, type 41 and press “Enter.”
Assume that you received a loan on July 1, 2007. The lender charges annual interest of 6%. On June 30, 2012, you owe the lender $802.93. Assuming that you made no payments for principal or interest on the loan during the five years, how much did you borrow?
Press “Enter” or click the left mouse button for solution.
8-40
Exercise 8-10Exercise 8-10Exercise 8-10Exercise 8-10
The present value of $802.93 at 6% for five years is $802.93 x 0.74726 = $600.
6%, 5 years
You borrowed $600.
8-41
55Determine the present value of an annuity.
ObjectiveObjectiveObjectiveObjective
8-42
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
Assume that you could purchase an investment that would pay $1,000 at the
end of each year for three years, and you expect to earn a return of 8%.
Assume that you could purchase an investment that would pay $1,000 at the
end of each year for three years, and you expect to earn a return of 8%.
How much would you be willing to pay for the investment?
8-43
$ 925.93 = $1,000 ÷ (1.08) $1,000
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
1
Present Value atBeginning of Year 1 End of Yr. 1
8-44
$ 925.93
857.34 = $1,000 ÷ (1.08) $1,000
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
Present Value atBeginning of Year 1 End of Yr. 2
2
8-45
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
Present Value atBeginning of Year 1 End of Yr. 3
3
$ 925.93
857.34
793.83 = $1,000 ÷ (1.08) $1,000
8-46
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
Present Value atBeginning of Year 1
$3,000.00 Total amount received over three years 2,577.10 Present value of total investment$ 422.90 Interest earned over three years
$ 925.93
857.34
793.83
$2,577.10 Present value of total investment
You would be willing to pay
$2,577.10.
You would be willing to pay
$2,577.10.
8-47
The PV function in Excel can be used to calculate the present value of an annuity. The function can be entered in the pop-up box or
directly into the cell.
The PV function in Excel can be used to calculate the present value of an annuity. The function can be entered in the pop-up box or
directly into the cell.
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
8-48
If you purchase an investment that paid $1,000 each year for three years at
8% interest, type =PV(0.08,3,–1000) in a cell
and press Enter.
If you purchase an investment that paid $1,000 each year for three years at
8% interest, type =PV(0.08,3,–1000) in a cell
and press Enter.
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
8-49
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
Or, you can use the present value
of an annuity table.
Or, you can use the present value
of an annuity table.
8-50
1
2
3
Interest Rate
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Period
2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.5313
Present Value of an AnnuityPresent Value of an AnnuityPresent Value of an AnnuityPresent Value of an Annuity
2.5772.577
PVA = FV x IFPVA = $1,000 x 2.577 (table value read to three decimal
places) PVA = $2,577 ($2,577.10 if five decimal places used)
0.990 0.981 0.971 0.962 0.952 0.943 0.935 0.926 0.917
1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759
8-51
A B C D FA B C D F
Present Value Present Value Interest EarnedInterest Earned Total AmountTotal Amount Value at Value at at Beginningat Beginning (Column B x(Column B x InvestedInvested End of End of
Year Year of Yearof Year Interest Rate)Interest Rate) (B + C)(B + C) YearYear
1 2,577.10 206.17 2,783.27 1,783.27
Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%
Exhibit 4Exhibit 4Exhibit 4Exhibit 4
$2,783.27 – $1,000.00Note: Column E was
omitted because of limited space.
8-52
A B C D FA B C D F
Present Value Present Value Interest EarnedInterest Earned Total AmountTotal Amount Value at Value at at Beginningat Beginning (Column B x(Column B x InvestedInvested End of End of
Year Year of Yearof Year Interest Rate)Interest Rate) (B + C)(B + C) YearYear
1 2,577.10 206.17 2,783.27 1,783.27
2 1,783.27 142.66 1,925.93 925.93
Exhibit 4Exhibit 4Exhibit 4Exhibit 4
$1,925.93 – $1,000.00
Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%
8-53
A B C D FA B C D F
Present Value Present Value Interest EarnedInterest Earned Total AmountTotal Amount Value at Value at at Beginningat Beginning (Column B x(Column B x InvestedInvested End of End of
Year Year of Yearof Year Interest Rate)Interest Rate) (B + C)(B + C) YearYear
1 2,577.10 206.17 2,783.27 1,783.27
2 1,783.27 142.66 1,925.93 925.93
3 925.93 74.07 1,000.00 0.00
TotalTotal 422.90422.90
Exhibit 4Exhibit 4Exhibit 4Exhibit 4 Interest Table for an Annuity of $1,000 at the End of Each Year for Three Years at 8%
8-54
Exercise 8-13Exercise 8-13Exercise 8-13Exercise 8-13
Click the button to skip this exercise.If you experience trouble making the button work, type 57 and press “Enter.”
A wealthy uncle has offered to give you either of two assets: (a) an asset that pays $500 at the end of three years or (b) an asset that pays $100 at the end of each year for five years. Assume that both assets earn a 7% annual rate of return. Which asset should you choose?
Press “Enter” or left click the mouse for solution.
8-55
Exercise 8-13Exercise 8-13Exercise 8-13Exercise 8-13
a. $500 x 0.81630 (from Table 3) = $408.15
7%, 3 years
b. $100 x 4.10020 (from Table 4) = $410.02
7%, 5 years
ContinuedContinuedContinuedContinued
8-56
Exercise 8-13Exercise 8-13Exercise 8-13Exercise 8-13
The annuity (b) has a slightly higher present value. The alternatives are approximately the same, however. (Note: One consideration may be expected investment opportunities at the end of three years. Since there is little difference between a. and b., a. may be the better choice since the $500 could be reinvested sooner than in b.)
8-57
66Determine investment values and interest expense or revenue for various periods.
ObjectiveObjectiveObjectiveObjective
8-58
Loan Payments and AmortizationLoan Payments and Amortization
You negotiate with a dealer to purchase a
car for $5,000, which you arrange to
borrow at the bank.
You negotiate with a dealer to purchase a
car for $5,000, which you arrange to
borrow at the bank.
8-59
The bank charges 12% interest on the loan, which is to be repaid in two years in equal monthly payments.
The bank charges 12% interest on the loan, which is to be repaid in two years in equal monthly payments.
Loan Payments and AmortizationLoan Payments and Amortization
How much will your payments be each month?
8-60
We are looking for the present value of multiple payments (an annuity),
therefore, Table 4 can be used to solve this problem.
We are looking for the present value of multiple payments (an annuity),
therefore, Table 4 can be used to solve this problem.
Loan Payments and AmortizationLoan Payments and Amortization
8-61
0.990 10 0.98039 0.97087 0.96154 0.95238
1.97040 1.94156 1.91347 1.88609 1.85941
2.94099 2.88388 2.82861 2.77509 2.72325
1
2
3
Interest RateInterest Rate
0.01 0.02 0.03 0.04 0.05 Period
24 21.24339 18.91393 16.93554 15.24696 13.79864
3
0.01
0.99010
1.97040
2.94099
0.01 0.01
0.99010
1.97040
2.94099
If the annual interest rate is 12 percent, then interest is 1 percent per month.
If the annual interest rate is 12 percent, then interest is 1 percent per month.
Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
21.24339
8-62
Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
24 21.24339 18.91393 16.93554 15.24696 13.7986421.24339
0.990 10 0.98039 0.97087 0.96154 0.95238
1.97040 1.94156 1.91347 1.88609 1.85941
2.94099 2.88388 2.82861 2.77509 2.72325
1
2
3
Interest RateInterest Rate
0.01 0.02 0.03 0.04 0.05 Period
3
0.01
0.99010
1.97040
2.94099
0.01 0.01
0.99010
1.97040
2.94099
24 21.24339 18.91393 16.93554 15.24696 13.79864
There are 24 monthly periods in two years.
There are 24 monthly periods in two years.
21.24339
8-63
Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization PVA = A x IF (Table 4)
$5,000 = A x 21.24339A = $5,000 ÷ 21.24339A = $235.37
24 21.24339 18.91393 16.93554 15.24696 13.7986421.24339
0.990 10 0.98039 0.97087 0.96154 0.95238
1.97040 1.94156 1.91347 1.88609 1.85941
2.94099 2.88388 2.82861 2.77509 2.72325
1
2
3
Interest RateInterest Rate
0.01 0.02 0.03 0.04 0.05 Period
3
0.01
0.99010
1.97040
2.94099
0.01 0.01
0.99010
1.97040
2.94099
24 21.24339 18.91393 16.93554 15.24696 13.7986421.24339
8-64
Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
Thus, the answer to the question
(How much would you pay each month?) is
$235.37.
Thus, the answer to the question
(How much would you pay each month?) is
$235.37.
8-65
Enter =PMT(.01,24,5000) in the cell and press Enter.Enter =PMT(.01,24,5000) in the cell and press Enter.
How would you determine the monthly car payment
by using the payment function in Excel?
How would you determine the monthly car payment
by using the payment function in Excel?
Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
8-66
Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
How much interest will you pay over the two years?
To answer this question, let’s walk through Exhibit 5 (p. 296)
from the textbook.
To answer this question, let’s walk through Exhibit 5 (p. 296)
from the textbook.
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A B C D FA B C D F
Present Value Present Value Interest IncurredInterest Incurred Value at Value at at Beginningat Beginning (Column B x(Column B x AmountAmount End of End of
MonthMonth of Yearof Year Interest Rate)Interest Rate) Paid)Paid) MonthMonth
1 5,000.00 50.00 235.37 4,814.63
Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5Exhibit 5Exhibit 5Exhibit 5
$5,000.00 – ($235.37 – $50.00)
Note: Column E was omitted
because of limited space.
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1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.41
Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5Exhibit 5Exhibit 5Exhibit 5
$4,814.63 – ($235.37 – $48.15)
A B C D FA B C D F
Present Value Present Value Interest IncurredInterest Incurred Value at Value at at Beginningat Beginning (Column B x(Column B x AmountAmount End of End of
MonthMonth of Yearof Year Interest Rate)Interest Rate) Paid)Paid) MonthMonth
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Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5Exhibit 5Exhibit 5Exhibit 5
TotalTotal 648.81648.81 5,648.815,648.81
1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32
23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00
A B C D FA B C D F
Present Value Present Value Interest IncurredInterest Incurred Value at Value at at Beginningat Beginning (Column B x(Column B x AmountAmount End of End of
MonthMonth of Yearof Year Interest Rate)Interest Rate) Paid)Paid) MonthMonth
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Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5Exhibit 5Exhibit 5Exhibit 5
TotalTotal 648.81648.81 5,648.815,648.81
1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32
23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00
A B C D EA B C D E
Present Value Present Value Interest IncurredInterest Incurred Value at Value at at Beginningat Beginning (Column B x(Column B x AmountAmount End of End of
MonthMonth of Yearof Year Interest Rate)Interest Rate) Paid)Paid) MonthMonth
The total interest incurred over the life of the loan is $648.81.
The total interest incurred over the life of the loan is $648.81.
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Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
Now let’s determine the
transactions that the bank and the
borrower would record each month.
Now let’s determine the
transactions that the bank and the
borrower would record each month.
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Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
The first transaction on April 1 records the amount of the
loan. The second transaction, dated April 30, records the
amount received from you, the customer, and the amount
earned for the first month, $50 ($5,000 x .12 x 1/12).
The first transaction on April 1 records the amount of the
loan. The second transaction, dated April 30, records the
amount received from you, the customer, and the amount
earned for the first month, $50 ($5,000 x .12 x 1/12).
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Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
JournalJournal Date Accounts Debits Credits
Apr. 1 Notes Receivable 5,000.00 2007 Cash 5,000.00Apr. 30 Cash 235.37 2007 Notes Receivable 185.37
Interest Revenue 50.00
Click this button or type “88” and press “Enter” to review the amortization table.
Bank’s BooksBank’s BooksBank’s BooksBank’s Books
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Loan Payments and AmortizationLoan Payments and Amortization
Bank’s BooksBank’s BooksBank’s BooksBank’s Books
Effect on Accounting EquationEffect on Accounting Equation
A = L +
4/1 Notes Receivable +5,000.00Cash –5,000.00
4/30 Cash 235.37Notes Receivable –185.37Interest Revenue +50.00
OE CC + RE
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Loan Payments and AmortizationLoan Payments and Amortization
Customer’s BooksCustomer’s BooksCustomer’s BooksCustomer’s Books
JournalJournal Date Accounts Debits Credits
Apr. 1 Cash 5,000.00 2007 Notes Payable 5,000.00Apr. 30 Notes Payable 185.37 2007 Interest Expense 50.00
Cash 235.37
Click this button or type “89” and press “Enter” to review the amortization table.
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Loan Payments and AmortizationLoan Payments and Amortization
Customer’s BooksCustomer’s BooksCustomer’s BooksCustomer’s Books
Effect on Accounting EquationEffect on Accounting Equation
A = L +
4/1 Cash +5,000.00Notes Payable +5,000.00
4/30 Notes Payable –185.37Interest Expense –50.00
Cash –235.37
OE CC + RE
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Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
In the last month of the loan (March 2009), the
bank records would reflect that the note has been fully paid by the
customer.
In the last month of the loan (March 2009), the
bank records would reflect that the note has been fully paid by the
customer.
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JournalJournal Date Accounts Debits Credits
Mar. 31 Cash 235.30 2009 Notes Receivable 232.97
Interest Revenue 2.33
Loan Payments and AmortizationLoan Payments and AmortizationLoan Payments and AmortizationLoan Payments and Amortization
Bank’s BooksBank’s BooksBank’s BooksBank’s BooksClick this button or type “90” and press “Enter” to review the amortization table.
8-79
Loan Payments and AmortizationLoan Payments and Amortization
Bank’s BooksBank’s BooksBank’s BooksBank’s Books
Effect on Accounting EquationEffect on Accounting Equation
A = L +
3/31 Cash +235.30Notes Receivable –232.97Interest Revenue +2.33
OE CC + RE
8-80
Unequal PaymentsUnequal PaymentsUnequal PaymentsUnequal Payments
Jill Johnson invested a portion of her salary at the beginning of each year for four years.
Jill Johnson invested a portion of her salary at the beginning of each year for four years.
The amounts she invested in those years were $700, $800, $900, and
$1,000, respectively.
The amounts she invested in those years were $700, $800, $900, and
$1,000, respectively.
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Unequal PaymentsUnequal PaymentsUnequal PaymentsUnequal Payments
How much would her investments be worth at the end of four years if
she earned 6% per year?
How much would her investments be worth at the end of four years if
she earned 6% per year?
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$ 833.71
$800 898.88
$900 954.00
$1,000 1,000.00
$700 Four Yearsx 1.19102 (6%, 3 periods)x 1.19102 (6%, 3 periods)
Three Yearsx 1.12360 (6%, 2 periods)x 1.12360 (6%, 2 periods)
Two Yearsx 1.0600 (6%, 1 period)x 1.0600 (6%, 1 period)
Unequal PaymentsUnequal PaymentsUnequal PaymentsUnequal Payments
x 1.0000x 1.0000
Total $3,686.59
Year
1
2
3
End of
4
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You can purchase an investment that is expected to pay $200, $300,
and $400 at the end of the next three years. You expect to earn 7%
interest. How much should you pay for the investment?
You can purchase an investment that is expected to pay $200, $300,
and $400 at the end of the next three years. You expect to earn 7%
interest. How much should you pay for the investment?
Unequal PaymentsUnequal PaymentsUnequal PaymentsUnequal Payments
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$200$186.92 One Yearx 0.93458x 0.93458
Two Years262.03 $300x 0.87344x 0.87344
$400326.52 Three Yearsx 0.81630x 0.81630
$775.47 Total
PV at Beginning
of YearAmounts Received at End of Each Year
Unequal PaymentsUnequal PaymentsUnequal PaymentsUnequal Payments
8-85
Future and Present Value Concepts
Exhibit 6Exhibit 6Exhibit 6Exhibit 6
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THE ENDTHE END
CCHAPTERHAPTER 8 8
8-87
8-88
Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5Exhibit 5Exhibit 5Exhibit 5
1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32
23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00
A B C D EA B C D E
Present Value Present Value Interest IncurredInterest Incurred Value at Value at at Beginningat Beginning (Column B x(Column B x AmountAmount End of End of
MonthMonth of Yearof Year Interest Rate)Interest Rate) Paid)Paid) MonthMonth
Click this button or type 73 and press “Enter” to return to Slide 73.
8-89
Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5Exhibit 5Exhibit 5Exhibit 5
1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32
23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00
A B C D EA B C D E
Present Value Present Value Interest IncurredInterest Incurred Value at Value at at Beginningat Beginning (Column B x(Column B x AmountAmount End of End of
MonthMonth of Yearof Year Interest Rate)Interest Rate) Paid)Paid) MonthMonth
Click this button or type 75 and press “Enter” to return to Slide 75.
8-90
Amortization Table for Automobile Loan of $5,000 for 24 Months at 1% per Month
Exhibit 5Exhibit 5Exhibit 5Exhibit 5
1 5,000.00 50.00 235.37 4,814.632 4,814.63 48.15 235.37 4,627.413 4,627.41 46.27 235.37 4,438.32
23 463,70 4.64 235.37 232.9724 232.97 2.33 235.30 0.00
A B C D EA B C D E
Present Value Present Value Interest IncurredInterest Incurred Value at Value at at Beginningat Beginning (Column B x(Column B x AmountAmount End of End of
MonthMonth of Yearof Year Interest Rate)Interest Rate) Paid)Paid) MonthMonth
Click this button or type 78 and press “Enter” to return to Slide 78.